A Practical View on Renaming

We revisit variable renaming from a practitioner's point of view, presenting concepts we found useful in dealing with operational semantics of pure Prolog. A concept of relaxed core representation is introduced, upon which a concept of prenaming is built. Prenaming formalizes the intuitive practice of renaming terms by just considering the necessary bindings, where now some passive "bindings" x/x may be necessary as well. As an application, a constructive version of variant lemma for implemented Horn clause logic has been obtained. There, prenamings made it possible to incrementally handle new (local) variables.Comment: In Proceedings WLP'15/'16/WFLP'16, arXiv:1701.0014

Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems

A narrowing tree for a constructor term rewriting system and a pair of terms is a finite representation for the space of all possible innermost-narrowing derivations that start with the pair and end with non-narrowable terms. Narrowing trees have grammar representations that can be considered regular tree grammars. Innermost narrowing is a counterpart of constructor-based rewriting, and thus, narrowing trees can be used in analyzing constructor-based rewriting to normal forms. In this paper, using grammar representations, we extend narrowing trees to syntactically deterministic conditional term rewriting systems that are constructor systems. We show that narrowing trees are useful to prove two properties of a normal conditional term rewriting system: one is infeasibility of conditional critical pairs and the other is quasi-reducibility